QI Wu

activity

20212026

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9 papers · 1 filter

math.CO2026

Strict spectral supersaturation for cliques: extremal graphs and sharp thresholds

Qi Wu, Yong Lu

For every fixed $r \geq 3$ and all sufficiently large $n$ , we determine the largest adjacency spectral radius of an $n$ -vertex graph with fewer than $q c_{r} (n)$ copies of $K_{r + 1}$ , wh…

math.LO2026

A cardinal trichotomy for topological equivalence classes of countable trees

Qi Wu, Yong Lu

For a tree $T$ , let $[T]$ be the set of isomorphism classes of trees that are mutually topological minors of $T$ . Bruno and Szeptycki proved that every locally finite tree satisfie…

math.CO2026

Exact random covers of metric trees: balanced rounding, duality, and sharp thresholds

Qi Wu, Yong Lu

Norin and Turcotte's asymptotically sharp bound for graph burning [J. Combin. Theory Ser. B 168 (2024), 208--235] led them to an exact random-cover conjecture for finite metric tre…

math.CO2026

A Proof of the Chen--Raspaud Conjecture

Qi Wu, Yong Lu

For every integer $k \geq 2$ , Chen and Raspaud conjectured that each graph $G$ with odd girth $\og(G)\ge2k+1$ and maximum average degree $\mad(G)<2+1/k$ has a $(2 k + 1 : k)$ -coloring. In…

math.CO2026

Every fork-free graph is perfectly weight divisible

Feng Liu, Shuang Sun, Yan Wang +2

A graph $G$ is \emph{perfectly weight divisible} if, for every positive integral weight function on $V (G)$ and every induced subgraph $H$ of $G$ with at least one edge, the vertex…

math.CO2026

Hamiltonian cycles in 7-tough $(P_{4} \cup P_{1})$ -free graphs

Yong Lu, Qi Wu, Qiannan Zhou

Shan~[J. Graph Theory (2026)] proved that every 23-tough $(P_{4} \cup P_{1})$ -free graph on at least three vertices is Hamiltonian. We improve this bound to 7 by replacing the final cut…

math.CO2026

Exact generalized Turán number of vertex-disjoint paths of length two

Qi Wu, Long-Tu Yuan

We determine the generalized Turán number of vertex-disjoint paths of length two and characterize all corresponding extremal graphs. Our proof combines the Lovász form of the Krusk…

math.CO2026

Local Turán inequalities for walks and the spectral radius

Feng Liu, Shuang Sun, Yan Wang +1

Nikiforov's well-known spectral Turán inequality for walks states that, for every graph $G$ with clique number $ω (G)$ , $λ^{r} (G) \leq w_{r} (G) (1 - 1/ ω (G))$ , where $λ (G)$ is the largest eig…

math.CO2026

Triangles in graphs without the expansion of $4$ -cycle

Jialei Song, Qi Wu, Long-Tu Yuan

The expansion $F^{△}$ of a graph $F$ is the graph obtained from $F$ by replacing each edge with a triangle. Lv \etal proposed a conjecture on the maximum number of triangle…

Strict spectral supersaturation for cliques: extremal graphs and sharp thresholds

A cardinal trichotomy for topological equivalence classes of countable trees

Exact random covers of metric trees: balanced rounding, duality, and sharp thresholds

A Proof of the Chen--Raspaud Conjecture

Every fork-free graph is perfectly weight divisible

Hamiltonian cycles in 7-tough (P4​∪P1​)-free graphs

Exact generalized Turán number of vertex-disjoint paths of length two

Local Turán inequalities for walks and the spectral radius

Triangles in graphs without the expansion of 4-cycle

Hamiltonian cycles in 7-tough $(P_{4} \cup P_{1})$ -free graphs

Triangles in graphs without the expansion of $4$ -cycle